let S be satisfying_Tarski-model TarskiGeometryStruct ; :: thesis: for a, b, c, d, p being POINT of S st between4 a,b,c,d & between c,p,d holds
between5 a,b,c,p,d
let a, b, c, d, p be POINT of S; :: thesis: ( between4 a,b,c,d & between c,p,d implies between5 a,b,c,p,d )
assume A1: ( between4 a,b,c,d & between c,p,d ) ; :: thesis: between5 a,b,c,p,d
then ( between a,p,d & between a,c,p & between b,c,p & between b,p,d & between c,p,d ) by Satz3p5p1, Satz3p5p2;
hence between5 a,b,c,p,d by A1, Satz3p5p1; :: thesis: verum